How do you solve using gaussian elimination or gauss-jordan elimination, #2x–3y+2z=2#, #x+4y-z=9#, #-3x+y–5z=5#?

1 Answer
Feb 14, 2018

Answer:

#x=115/31#, #y=32/31# and #z=-36/31#

Explanation:

Perform the Gauss Jordan elimination on the augmented matrix

#A=((2,-3,2,|,2),(1,4,-1,|,9),(-3,1,-5,|,5))#

I have written the equations not in the sequence as in the question in order to get #1# as pivot.

Perform the folowing operations on the rows of the matrix

#R1larrR1-2R2#; #R3larrR3+3R2#

#A=((0,-11,4,|,-16),(1,4,-1,|,9),(0,13,-16,|,32))#

#R3larr(R3+R1)#

#A=((0,-11,4,|,-16),(1,4,-1,|,9),(0,2,-12,|,16))#

#R3larr(R3)/2#

#A=((0,-11,4,|,-16),(1,4,-1,|,9),(0,1,-6,|,8))#

#R1larrR1+11R3; R2larrR2-4R3#

#A=((0,0,-62,|,72),(1,0,23,|,-23),(0,1,-6,|,8))#

#R1larr(R1)/(-62)#

#A=((0,0,1,|,-36/31),(1,0,23,|,-23),(0,1,-6,|,8))#

#R2larrR2-23R1; R3larrR3+6R1#

#A=((0,0,1,|,-36/31),(1,0,0,|,115/31),(0,1,0,|,32/31))#

Thus, #x=115/31#, #y=32/31# and #z=-36/31#